Corporate FinanceCorporate Finance

Lecture 5Lecture 5

Topics coveredTopics covered

Decision treesDecision trees Dealing with uncertaintyDealing with uncertainty

– Sensitivity analysisSensitivity analysis– Senario analysisSenario analysis

Decision TreesDecision Trees

Graphically represent Graphically represent the alternatives the alternatives available to us in available to us in each period and the each period and the likely consequences likely consequences of our actions.of our actions.

This graphical This graphical representation helps representation helps to identify the best to identify the best course of action.course of action.

Example of Decision TreeExample of Decision Tree

Do not study

Study finance

“C”

“A”

“B”

“F”

“D”

Decision treesDecision trees

Example:Example:– The test marketing for a new project will take The test marketing for a new project will take

one year and will cost $100 million. one year and will cost $100 million. – There is a 75% chance that the test will be There is a 75% chance that the test will be

successful.successful.– If successful, the project will be taken and the If successful, the project will be taken and the

NPV is estimated to be $1,517 million at NPV is estimated to be $1,517 million at year=1.year=1.

– If not successful, the project will have an NPV If not successful, the project will have an NPV of $-3,611 million at year=1.of $-3,611 million at year=1.

– The discount rate is 15% for the firm.The discount rate is 15% for the firm.

Decision treesDecision trees

Test result

revealed

Success

failure

InvestNPV=1517

No investNPV=0

InvestNPV=-3611

No investNPV=0

Now

Test marketing

-$100 million

Year 1

Investment

test

No test

75%

25%

1. Test or not 2. Invest or not

Decision treesDecision trees

How to solve the problemHow to solve the problem– Make decisions in Make decisions in reversereverse order with order with

decision treesdecision trees

Decision treesDecision trees

Test result

revealed

Success

failure

InvestNPV=1517

No investNPV=0

InvestNPV=-3611

No investNPV=0

Now

Test marketing

-$100 million

Year 1

Investment

test

No test

75%

25%

1. Test or not 2. Invest or not

Decision treesDecision trees

Test result

revealed

Success

failure

InvestNPV=1517

No investNPV=0

InvestNPV=-3611

No investNPV=0

Now

Test marketing

-$100 million

Year 1

Investment

test

No test

75%

25%

1. Test or not 2. Invest or not

X

Decision treesDecision trees

Test result

revealed

Success

failure

InvestNPV=1517

No investNPV=0

InvestNPV=-3611

No investNPV=0

Now

Test marketing

-$100 million

Year 1

Investment

test

No test

75%

25%

1. Test or not 2. Invest or not

X

Decision treesDecision trees

Test result

revealed

Success

failure

InvestNPV=1517

No investNPV=0

InvestNPV=-3611

No investNPV=0

Now

Test marketing

-$100 million

Year 1

Investment

test

No test

75%

25%

1. Test or not 2. Invest or not

X

X

Decision treesDecision trees

Test result

revealed

Success

failure

InvestNPV=1517

No investNPV=0

Now

Test marketing

-$100 million

Year 1

Investment

test

No test

75%

25%

1. Test or not 2. Invest or not

E[Payoff]1=0.75*1517+0.25*0=1138

NPV=-100+1138/1.15=890>0

How to handle How to handle uncertaintyuncertainty Sensitivity AnalysisSensitivity Analysis

– Analyze the effects of changes in Analyze the effects of changes in one variable (e.g. sales, cost, one variable (e.g. sales, cost, discount rate) on a project.discount rate) on a project.

Scenario AnalysisScenario Analysis – Project analysis given a particular Project analysis given a particular

combination of assumptions.combination of assumptions.

How to handle How to handle uncertaintyuncertainty

ExampleExample

Given the Given the expected expected cash flow forecastscash flow forecasts listed on the next slide, listed on the next slide, determine the NPV of determine the NPV of the project given the project given changes in the cash changes in the cash flow components using flow components using an 8% cost of capital. an 8% cost of capital.

How to handle How to handle uncertaintyuncertainty

7805,400-FlowCash Net

780flowcash Operating

330after taxProfit

22040% @ .Taxes

550profitPretax

450onDepreciati

2,000Costs Fixed

13,000Costs Variable

16,000Sales

5,400-Investment

12-1 Years0Year

NPV= $478

How to handle How to handle uncertaintyuncertainty

Possible OutcomesPossible Outcomes

1,9002,0002,100)Costs(000s Fixed

80%81.25%83%sales) of (%Cost Var

18,00016,00014,000)Sales(000s

5,0005,4006,200(000s)Investment

OptimisticExpectedcPessimistiVariable

Range

Sensitivity AnalysisSensitivity Analysis

Assuming change in Assuming change in Investment Investment

7806,200-FlowCash Net

780flowcash Operating

330after taxProfit

22040% @ .Taxes

550profitPretax

450onDepreciati

2,000Costs Fixed

13,000Costs Variable

16,000Sales

6,200-Investment

12-1 Years0Year

NPV= ($322)

($400.00)

($200.00)

$0.00

$200.00

$400.00

$600.00

$800.00

$1,000.00

-6200 -6000 -5800 -5600 -5400 -5200 -5000

investment

NP

V

Scenario AnalysisScenario Analysis

2,018,000-478,000NPV

3,382,0005,878,000flowscash of luePresent va

448,000780,0007)(4 operations from flow8.Cash

1,200-330,000after taxProfit 7.

800-220,0006.Taxes

2,000-550,0004)-3-2-(1profit Pretax 5.

450,000450,000onDepreciati 4.

2,000,0002,000,000costs 3.Fixed

11,152,00013,000,000costs Variable 2.

000,600,13000,000,16Sales 1.

Scenario. Store CompetingCase. Base